These snippets are not very helpful and certainly don't give arrivals but you may find them useful IF they relate to the same chap, although it looks as though there may have been more than on George AYLWIN in Tasmania early on.
A George AYLWIN was listed as the licensee of
The Ship Inn, Launceston in 1833. A George AYLWIN is shown arriving in Launceston per ship
Prince Regent, 13 October 1829.
Geoerge AYLWIN is appointed District Constable at Launceston, 1826
http://trove.nla.gov.au/ndp/del/article/8790628In
1826 1828 a George AYLWIN of the Cumberland Arms, George St Sydney announces that he has commenced business as a candle maker in Sydney. A bit of a long shot but could this be the chap who was a tallow chandler in Hobart? However if he is being made a Constable in Launceston the same year ..... IF it is the same man..............

http://trove.nla.gov.au/ndp/del/article/8790628
http://trove.nla.gov.au/ndp/del/article/31760568(Edit to correct.)THe Sydney candle maker takes on Mr Cole as a partner.
http://trove.nla.gov.au/ndp/del/article/36864803In March 1829 Geroge AYLWIN sells the business to John Cole.
http://trove.nla.gov.au/ndp/del/article/2191935October 1829 shows Mr George AYLWIN arriving at Launceston from Sydney, on the brig
Prince Regent (As noted above)
http://trove.nla.gov.au/ndp/del/article/84778581There is mention of Mrs
Harriet AYLWIN (who is listed as the wife of George - see above) leaving for
Valparaiso on the
Esparanza, November 1836. I'm not 100% sure but it seems the ship left from Hobart so possibly there is a connection.
http://trove.nla.gov.au/ndp/del/article/12856988There are hardly any further mentions which seem relevant after this one, although land belonging to "AYLWIN" in Tasmania is mentioned once or twice